In this paper we propose a formalized mathematical model to analyze the dynamic aspect of the semiotic behavior of political actors in dialogic forms of interaction, such are presidential TV debates, from an interdisciplinary perspective that brings together: positioning theory (Davies and Harré, 1990; Harré and Moghaddam 2016), multimodality (Maricchiolo et al. 2013; Gnisci et al. 2013; Navarretta and Paggio 2013) and functional theory of political campaign discourse (Benoit and Wells 1996; Benoit 2014, 2016). We are interested in how the political actors involved in such forms of communication manage the persuasive potential (Benoit 2014) of discourse to position themselves in a credible way, as a political persona in front of the public, through various strategies of complementarity of the semiotic resources.